cp's OEIS Frontend

A154279 List of pairs (a(n),b(n)): a(n) = prime(n) - prime(n-1) + a(n-1); b(n) = (prime(n) - prime(n-1))*b(n-1).

%I A154279 #10 Sep 09 2016 14:11:31
%S A154279 0,1,2,1,3,1,5,2,7,4,11,16,13,32,17,128,19,256,23,1024,29,6144,31,
%T A154279 12288,37,73728,41,294912,43,589824,47,2359296,53,14155776,59,
%U A154279 84934656,61,169869312,67,1019215872,71,4076863488,73,8153726976,79,48922361856,83
%N A154279 List of pairs (a(n),b(n)): a(n) = prime(n) - prime(n-1) + a(n-1); b(n) = (prime(n) - prime(n-1))*b(n-1).
%C A154279 There are primes associated with the product sequence:
%C A154279 Flatten[Table[If[PrimeQ[b[n] - 1], b[n] - 1, If[PrimeQ[b[n] + 1], b[ n] + 1, {}]], {n, 0, 30}]].
%C A154279 {2, 2, 2, 3, 3, 17, 31, 127, 257, 6143, 12289, 73727, 294911, 14155777, 169869311, 4076863487, 1174136684543}
%H A154279 G. C. Greubel, <a href="/A154279/b154279.txt">Table of n, a(n) for n = 0..1001</a>
%F A154279 {a(n),b(n)}:
%F A154279 a(n) = Prime[n] - Prime[n-1] + a(n-1);
%F A154279 b(n) = ( Prime[n] - Prime[n-1] )*b(n-1).
%t A154279 a[0] = 0; a[1] = 2; a[n_] := a[n] = Prime[n] - Prime[n - 1] + a[n - 1];
%t A154279 b[0] = 1; b[1] = 1; b[n_] := b[n] = (Prime[n] - Prime[n - 1])*b[n - 1];
%t A154279 Flatten[Table[{a[n], b[n]}, {n, 0, 30}]]
%o A154279 (PARI) a(n)=if(n<4, return(if(n>2,1,n))); my(k=n\2,p=prime(k-1),q=nextprime(p+1)); if(n%2, (q-p)*a(n-2), q-p + a(n-2)) \\ _Charles R Greathouse IV_, Sep 09 2016
%Y A154279 Cf. A081411.
%K A154279 nonn,tabf,less
%O A154279 0,3
%A A154279 _Roger L. Bagula_, Jan 06 2009